Functional–structural plant modelling

Authors


In the last decade, many research teams throughout the world initiated a new approach in plant science by developing computer models of plant functioning and growth. The intention of this approach was to understand the complex interactions between plant architecture and the physical and biological processes that drive the plant development at several spatial and temporal scales, using so-called functional–structural plant models (FSPMs). Explicitly taking into account the spatial distribution of plant organs has multiple consequences: (i) FSPMs are usually associated with 3D plant models where plant architecture is represented as a collection of interconnected plant components, which are distributed in the 3D below- and above-ground space; (ii) FSPMs usually deal with the spatial distribution of both environmental and biological processes; (iii) FSPMs are usually based on scaling up, mostly from the organ to the plant, but also from tissue to organ or from plant to stand; and (iv) to deal with the system complexity owing to the high number of plant constituents, and to deal with the potentially high numbers of interacting processes, FSPMs must develop adequate computational methods.

To discuss these questions, in 1996 the FSPM series of workshops (http://amap.cirad.fr/workshop/FSPM04/index.html) was established to assemble regularly from all over the world scientists who integrate 3D representations of plants, physiological models, environmental models, computer science and mathematics into their approach. The general aim of this community is to understand better, through the use of 3D representations, the importance of taking into account the spatialisation of processes in plant functioning and morphogenesis. The FSPM community contributes to unravelling these integrated plant functioning mechanisms and in this issue of New Phytologist we feature a set of papers that address the different aspects and questions raised (Godin et al., 2005), so highlighting the current advances and future directions required.

‘Plant spatial representations can be made at various levels of detail, ranging from accurate descriptions of each organ to coarse descriptions of branching systems at plant level.’

Nature of plant spatial representation

This question is central to the design of FSPMs. Plant spatial representations can be made at various levels of detail, ranging from accurate descriptions of each organ (leaf, metamer, etc.) to coarse descriptions of branching systems at plant level. Plant organs may be represented as constituents simply distributed in space. This geometric representation can be augmented by a description of the physical connections between organs, corresponding to the plant topological structure. Geometric structures are useful to model interactions of the plant with its environment. Topological structures are useful to model the circulation of substances or physical quantities within the plant (water, sugars, strains, etc.).

Different methods have been designed to digitise plants of various sizes in 3D or to map their topological structures (Sinoquet & Rivet, 1997) (Godin et al., 1999) (Hanan & Wang, 2004). Using these methods, researchers can build up plant architecture databases that are used for further analysis or modelling. To analyse these complex databases, dedicated tools are necessary. Durand et al. (pp. 813–825, this issue) give a very innovative illustration of such analysis tools. They introduce a new Markovian-based stochastic model designed to identify homogeneous zones in tree structures and transitions between these zones. This approach contributes to creating a new generation of tools for automating complex tree architecture analysis in the context of understanding the botanical organisation of plants or building and assessing models.

Plant structure as an interface

The surfaces of plant organs are the location of energy, mass and information exchanges with the environment. From the plant viewpoint, this includes phylloclimate (Chelle, pp. 781–790, this issue), which is the microclimate and the environmental signals sensed by plants at the organ scale, and includes mass and energy fluxes gained or lost by the plant. From the environment point of view, plants act as modifiers of both soil and microclimate variables, as the result of plant presence (e.g. light interception, wind attenuation, disease propagation) and also due to tree functioning (e.g. air humidity due to transpiration, soil drying). Most of the interactions between the plant and the environment only depend on plant geometry, namely the 3D distribution of plant organs (e.g. light interception). In particular, the plant ability for resource capture mainly depends on spatial display by foraging organs. However, plant topology also influences the interactions between the plant and the environment. By using a FSPM, Pearcy et al. (pp. 791–800, this issue) show how light-capture strategies are influenced by topological constraints, namely hydraulics and biomechanics, and how plants regulate biomass investment in order to achieve multiple purpose optimisation. This illustrates the usefulness of FSPMs to understand interactions between multiple processes better.

Plant as a network

The plant structure provides the support for different forms of fluxes (water, sugars) and signals (mechanical constraints, hormones) that control the plant functioning and growth. Models of water transport have been developed in the past decade and rely on the application of Darcy's law to express the relationship between fluxes and water potential in porous media, (e.g. Früh & Kurth, 1999). More recently, the simulation of mechanical stress and strains in plants has been considered by several teams (Jirasek et al., 2000; Alméras et al., 2002; Fourcaud & Lac, 2003) and is now considered to be a tractable issue. The problem of carbon transport and allocation is more complex because the underlying physiological processes are difficult to observe and are not yet well understood. Current modelling approaches use different variants of the concept of source and sink strength, reviewed in this issue by Minchin & Lacointe (pp. 771–779, this issue). The authors suggest that a ‘minimal Münch model’ can provide a sound and general theoretical framework to model carbon transport, where allocation priorities are an emergent property of the model. Allen et al. (pp. 869–880, this issue) illustrate this approach by describing a transport-resistance model based on the integration of similar assumptions for carbohydrate flow and allocation and l-systems for studying the growth of peach trees.

Plant as a developing organism

The growth of the plant continuously modifies the network of components and space occupation, which in turn changes the general balance between organ demand and production. This dynamic feedback between structure and function is probably one key issue in the understanding of plant development which necessitates further theoretical and applied developments. Current work in this area consists of developing mechanistic models that integrate models of physiological processes and descriptive information where knowledge of the underlying mechanisms is lacking. Knowledge is usually expressed at the metamer or growth unit level, and the growth of the entire organism is considered as an emerging property of the locally defined interactions between plant components or between plant components and environmental factors.

Two approaches in this issue were designed to study the effect of environmental factors (here, light) on plant growth. Evers et al. (pp. 801–812, this issue) adopted a detailed descriptive approach to model the growth of wheat. The variation of architectural variables throughout time (e.g. leaf dimensions, internode length, phyllochrone and leaf number) was estimated according to field measurements or bibliographic data. Sterck et al. (pp. 827–843, this issue) designed a model where each metamer can produce a flush of growth. Flushes are controlled by the product of probabilities, depending on their metamer topological and environmental context. This growth principle is then integrated with computation of light capture, photosynthesis and carbon allocation at each cycle of growth to study the effect of different light environment on tree growth.

Models of plant development can also be used to study the ability of locally specified hypotheses to generate a range of emerging behaviours through complex interaction at plant level. Fournier et al. (pp. 881–894, this issue) describes a model of grass leaf that was designed to analyse the likelihood of event synchronisation during plant growth, such as leaf emergence and triggering of leaf elongation. Allen et al. developed a model able to integrate various sources of physiological knowledge. Here, emphasis is put on the handling of complex dynamical systems. First, efficient algorithms are described to compute carbohydrate flows within the dynamically changing tree structure. Second, correct qualitative behaviour of the model is shown to emerge from simple quantitative local rules expressing carbon allocation and storage, water supply, light availability and fruit growth.

Finally, the approach of Buck-Sorlin et al. (pp. 859–867, this issue) shows the possibility of using growth models to test the integration of new levels of knowledge in a complex system. Their model combines morphogenetic rules of the development of Barley and a description of metabolic regulatory network simulating the biosynthesis of gibberellic acids that control the elongation of internodes.

Challenges and future directions of research

Functional–structural approaches are intended to face several aspects of plant architecture complexity: (i) complexity of the biological system, in particular due to the high variability and plasticity of plant growth, and to the multitude of interwoven scales at which physical, ecophysiological and morphogenetic phenomena occur; (ii) complexity of integrating various sources of knowledge, possibly at different time scales, into one consistent modelling framework; and (iii) computer simulation complexity, which necessitates management of numerous dynamically changing and interacting parts. These questions are currently being discussed within the FSPM research community (Godin et al., 2004), where the following new approaches are emerging.

Integration.  To tackle the lack of a modelling framework for developing integration of structure and function, new modelling paradigms are being developed and tested. This is illustrated for instance by the intermediate-level approach (not completely mechanistic and not completely descriptive), based on a systematic flux-based representation of the various phenomena at different scales (Renton et al., pp. 845–857, this issue).

Link between models and the real world.  Because virtual plants and FSPMs are firstly tools developed to address biological questions, they must show properties and behaviours similar to those of real plants. FSPMs allow scientists to make virtual experiments and measurements, impossible to set in the real world due to time, cost or feasibility constraints. Light partitioning between fruiting units in tree canopies, for example, cannot be measured from light sensors distributed in the canopy, whereas virtual plants allow accurate estimations of light sharing at intra-canopy scales (Allen et al.). In order for there to be confidence in the results from the virtual experiments, quality requirements are needed. This should be carefully checked from quantitative assessment. This applies for both plant structure and function. As a result, virtual experiments should presently be used in applications where FSPMs results have been validated from comparison with field or lab measurements, while more interaction between modellers and experimenters should develop in order to ensure close relationships between FSPMs and real plants.

Understanding the effect of genes in the development of plant form.  The large number of recent results obtained in both molecular and cellular biology makes it possible to consider a new approach of developmental biology based on modelling at a cellular scale. Today, several teams are building models of meristem development, organ growth and hormone signals, to grasp the role of different parameters in the control of phenomena like phyllotaxy, meristem maintenance and response to environment (for a review, see Prusinkiewicz, 2004). A first step in this direction is illustrated by Buck-Sorlin et al.

Design of new languages and formalisms.  Several attempts are being made in order to generalise the l-system approach. Classical l-systems only manipulate strings or tree structures. However, at the scale of tissues for instance, structures correspond to complex 2D or 3D objects and cannot be simply represented by strings or trees. In an attempt to generalise l-systems to model the development of discretised surfaces, Prusinkiewicz and colleagues introduced a language, called VV, for rewriting meshes of triangles (representing tissues). They applied this generic system to the problem of modelling the growth of apical meristem and the emergence of phyllotactic patterns (Smith & Prusinkiewicz, 2004). In a similar perspective, Buck-Sorlin et al. introduce another extension of l-systems, RGG, that can represent genetic, metabolic and morphological aspects of plant development within the same framework.

Conclusion

The FSPM community is young and multidisciplinary in nature. Its size is increasing at each FSPM conference since 1996 and around 200 participants attended FSPM04 in Montpellier, June 2004. As illustrated by the selection of papers in this special feature of New Phytologist, major trends are readily observable: (i) l-systems, for instance, are adopted by a majority of teams as a paradigm to model plant development; (ii) there is a real need for modellers to exchange ideas, formalisms and experience independently of the type of plant (grass, bush or tree) they work on; and (iii) there is a new and growing interest in the FSPM community in modelling the interaction between genes and form. These trends will probably be the basis of major topics of the next FSPM conference, which will be held in New Zealand in November 2007.

Ancillary